Lab 8 – Active 2-D Arrays & Matrices

PSUC Lab 8 — Matrix Grid Operations

Active Logic: 2-Dimensional Arrays (Matrices)

Master 2D row-column indexing (mat[row][col]), student marks row/col accumulators, matrix searching, matrix multiplication, symmetry, trace, and norm.

2-D Matrix Rules

Concept	Rule / Formula	Key Trap / Pitfall
Indexing	`mat[i][j]` (i=row, j=col)	Do not confuse row index `i` with column index `j`!
Multiplication	`C[i][j] = ∑ (A[i][k] × B[k][j])`	Requires 3 nested loops! (i, j, k)
Symmetry	`A[i][j] == A[j][i]`	Matrix must be square (Rows = Cols)
Trace & Norm	`Trace = ∑ A[i][i]`, `Norm = √∑(A[i][j]²)`	Trace is diagonal sum, Norm is Frobenius norm

🎯 Learning Philosophy: Active Logic Building

Test your 2-D matrix logic across 3 Interactive Learning Modes:

🧠 Tab 1 (Logic & Hints): Matrix indices & multiplication rules.
🧩 Tab 2 (Logic Puzzle): Complete missing row/col loop bounds & matrix visualizers!
💻 Tab 3 (C Solution): Reference verified C code solutions.

Solve matrix puzzles before peeking at C source code!

Exercise 1 of 5

Student Marks Totals & Subject Averages

Computes row totals (total marks per student) and column averages (average marks per subject) in a 2D marks matrix.

Row vs Column Sum

Row Sum (Student Total): Outer loop i, inner loop j → sum += marks[i][j]
Column Sum (Subject Avg): Outer loop j, inner loop i → sum += marks[i][j]

Interactive Logic Hints

💡 Hint 1: Where to reset sum = 0? ▼

Reset sum = 0 INSIDE the outer loop before starting the inner loop for each row/column!

🧩 Complete Marks Accumulator Loops

// Student Total (Row Sum)
for (i = 0; i < 3; i++) {
  studentTotal = 0;
  for (j = 0; j < 3; j++) studentTotal += marks[][];
}
// Subject Average (Column Sum)
for (j = 0; j < 3; j++) {
  subSum = 0;
  for (i = 0; i < 3; i++) subSum += marks[][j];
}

Select matrix indices above and click Check!

📊 Marks Table Calculator

3 Students × 3 Subjects Grid:

Matrix output...

Totals & Averages...

student_marks.cReference C Code

#include <stdio.h>

int main() {
    int marks[3][3] = {{85, 90, 78}, {72, 88, 95}, {91, 65, 80}};
    int i, j, studentTotal;

    for (i = 0; i < 3; i++) {
        studentTotal = 0;
        for (j = 0; j < 3; j++) studentTotal += marks[i][j];
        printf("Student %d Total = %d\n", i + 1, studentTotal);
    }

    for (j = 0; j < 3; j++) {
        int subSum = 0;
        for (i = 0; i < 3; i++) subSum += marks[i][j];
        printf("Subject %d Avg = %.2f\n", j + 1, subSum / 3.0);
    }
    return 0;
}

Exercise 2 of 5

Search Element in 2-D Matrix

Searches a target key in 2-D matrix and returns its exact [row][col] position.

Matrix Search Traversal

Outer loop i = 0 to ROWS-1
Inner loop j = 0 to COLS-1
If mat[i][j] == key → found = true; row = i; col = j; break;

Interactive Logic Hints

💡 Hint 1: What is the time complexity of matrix search? ▼

Linear matrix search takes O(Rows × Cols) operations!

🧩 Complete Matrix Search Loop

bool found = false;
for (i = 0; i < R; i++) {
  for (j = 0; j < C; j++) {
    if (mat[i][j] key) {
      found = true; ;
    }
  }
}

Select statements above and click Check!

🔍 Matrix Key Search Engine

Enter Search Key:

Matrix grid...

Search result...

matrix_search.cReference C Code

#include <stdio.h>
#include <stdbool.h>

int main() {
    int mat[3][3] = {{10, 20, 30}, {40, 95, 60}, {70, 80, 90}};
    int key = 95, i, j, foundRow = -1, foundCol = -1;
    bool found = false;

    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            if (mat[i][j] == key) {
                found = true; foundRow = i; foundCol = j; break;
            }
        }
        if (found) break;
    }

    if (found) printf("Key %d found at row %d, col %d\n", key, foundRow, foundCol);
    else       printf("Key %d NOT found.\n", key);
    return 0;
}

Exercise 3 of 5

Matrix Multiplication (C = A × B)

Multiplies two matrices A_{r1 × c1} and B_{r2 × c2} (Requires c1 == r2).

3-Loop Multiplication Logic

Outer i: Row of matrix A
Middle j: Column of matrix B
Inner k: Dot product accumulator → C[i][j] += A[i][k] * B[k][j]

Interactive Logic Hints

💡 Hint 1: What is the condition for matrix multiplication? ▼

Number of columns in A MUST equal number of rows in B! (c1 == r2).

🧩 Complete Matrix Multiplication Dot Product

for (i = 0; i < r1; i++) {
  for (j = 0; j < c2; j++) {
    C[i][j] = 0;
    for (k = 0; k < c1; k++) {
      C[i][j] += A[i][] * B[][j];
    }
  }
}

Select inner dot product indices and click Check!

✖️ Matrix Multiplication Calculator

Matrix A & B product...

Result matrix...

matrix_mult.cReference C Code

#include <stdio.h>

int main() {
    int A[2][2] = {{1, 2}, {3, 4}};
    int B[2][2] = {{5, 6}, {7, 8}};
    int C[2][2], i, j, k;

    for (i = 0; i < 2; i++) {
        for (j = 0; j < 2; j++) {
            C[i][j] = 0;
            for (k = 0; k < 2; k++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    printf("Product Matrix C:\n%d %d\n%d %d\n", C[0][0], C[0][1], C[1][0], C[1][1]);
    return 0;
}

Exercise 4 of 5

Matrix Symmetry & Magic Square Verification

Verifies if a matrix is Symmetric (A[i][j] == A[j][i]) and if it forms a Magic Square (equal row, column, and diagonal sums).

Symmetry & Magic Rules

Symmetry: arr[i][j] == arr[j][i] for all i, j
Magic Square: All row sums = All col sums = Main diag sum = Anti diag sum

Interactive Logic Hints

💡 Hint 1: What is a famous 3x3 Magic Square sum? ▼

The standard 3x3 magic square sum using numbers 1-9 is 15!

🧩 Complete Matrix Symmetry Check

bool isSymmetric = true;
for (i = 0; i < n; i++) {
  for (j = 0; j < n; j++) {
    if (mat[i][j] mat[][]) {
      isSymmetric = false; break;
    }
  }
}

Select statements above and click Check!

🔮 Magic Square & Symmetry Tester

3x3 Test Matrix...

Symmetry & Magic status...

matrix_magic.cReference C Code

#include <stdio.h>
#include <stdbool.h>

int main() {
    int mat[3][3] = {{8, 1, 6}, {3, 5, 7}, {4, 9, 2}};
    int i, j;
    bool isSymmetric = true;

    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            if (mat[i][j] != mat[j][i]) { isSymmetric = false; break; }
        }
    }
    printf("Symmetric: %s\n", isSymmetric ? "YES" : "NO");
    return 0;
}

Exercise 5 of 5

Matrix Trace & Frobenius Norm

Computes Matrix Trace (Trace = ∑ A[i][i]) and Frobenius Norm (Norm = √∑(A[i][j]²)).

Trace & Norm Equations

Trace: Sum of main diagonal elements: trace += mat[i][i]
Norm: Square root of sum of squares: norm += mat[i][j] * mat[i][j], then sqrt(norm)

Interactive Logic Hints

💡 Hint 1: What header is needed for sqrt()? ▼

Include #include <math.h> and link math library (-lm)!

🧩 Complete Trace & Norm Logic

for (i = 0; i < n; i++) {
  trace += mat[][];
  for (j = 0; j < n; j++) {
    normSum += mat[i][j] * mat[i][j];
  }
}
double norm = (normSum);

Select functions above and click Check!

📐 Matrix Trace & Norm Calculator

3x3 Matrix...

Trace & Norm values...

matrix_trace_norm.cReference C Code

#include <stdio.h>
#include <math.h>

int main() {
    int mat[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    int i, j, trace = 0;
    double normSum = 0.0, norm;

    for (i = 0; i < 3; i++) {
        trace += mat[i][i];
        for (j = 0; j < 3; j++) {
            normSum += mat[i][j] * mat[i][j];
        }
    }
    norm = sqrt(normSum);
    printf("Trace = %d\nNorm  = %.2f\n", trace, norm);
    return 0;
}

Knowledge Check

Test Your 2-D Matrix Logic Mastery

Question 1 of 5

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